CAT 2025 Lesson : Class Discussion: Numbers - Number Systems: 1 to 8

Class Discussion - Number Systems

Question 1

37426 of the base 9 system when written in base 3 is

		1011021210
		1012120120
		1012210120
		1021110220

Question 2

In the base

x

number system, the product of 233 and 122 is 32056. The number 100 of the decimal system when written in base x is

Answer: 202

Question 3

How many 3-digit base 6 numbers are also 3-digit numbers when written in base 5 as well as base 7?

Answer: 76

Question 4

A certain weighing machine displaying the weight in grams is faulty. It always skips the digit 3 and moves directly to 4 after the digit 2. It also skips the number 7 and directly moves to 8 after the digit 6. When a sack of grains is weighed, the machine displays 5914 grams. What is the actual weight (in grams)?

Answer: 2507

Question 5

In a certain number system, sum of 2356 and 1413 is 4102. The number 1024 of this system when written in decimal system is

Answer: 361

Question 6

The average of

(41)_{7}

and

(32)_{5}

(32)_{B}

. Then B = ?

		5
		6
		7
		8

Question 7

The prime minister of a kingdom has been asked to place 400 coins into

n

sealed bags such that when the king asks for a certain number of coins, he has to handover the coins without opening the bags. If the king can ask for any number of coins between 1 and 400 (both inclusive), then what is the minimum value of

n

?

Answer: 9

Question 8

A positive whole number M less than 100 is represented in base 2 notation, base 3 notation, and base 5 notation. It is found that in all three cases the last digit is 1, while in exactly two out of the three cases the leading digit is 1. Then M equals
[CAT 2003 L]

		31
		63
		75
		91

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